Question

Use substitution to write an equivalent quadratic equation.

(3x + 2)2 + 7 (3x + 2) – 8 = 0
-
u2 + 74 - 8 = 0, where u = (3x + 2)2
u2 + 7u - 8 = 0, where u = 3x + 2
u2 + 70 - 8 = 0, where u = 7(3x + 2)
lu² +4-8=0
What’s the answer?

Answer 1

second option:
`u^(2)+7u-8=0`

Explanation:

We have the equation given:

`(3x+2)^(2)+7(3x+2)-8=0`

We can replace the variable in the quardatic equation.

So,

`Putting\\u=3x+2`

Putting u in place of 3x+2 will give us:

`(u)^(2)+7(u)-8=0`

So the answer is:

`u^(2)+7u-8=0`

So, the second option is correct ..

Answer 2

For this case we can make a change of variable, to obtain a quadratic equation of the form:

`ax ^ 2 + bx + c = 0`

Making the change:
`u = 3x + 2`

Substituting the change we have:

`u ^ 2 + 7u-8 = 0`

Thus, the correct option is:
`u ^ 2 + 7u-8 = 0`where
`u = 3x + 2`

Answer:

Option B